related rates of change (please help ASAP)

G

Guest

Guest
i needed help with understanding related rates of change...
i have this problem:
"A spherical balloon is inflated with gas at the rate of 800 cubic centimeters per minute. How fast is the radius of the balloon increasing at the instant the radius is 30 centimeters?"

so far i've gotten:
(dV/dt)=4(pi)(30cm)^2(800cm^3/min)

and then for my answer i got:
2,880,000cm/min

is this right???
 
if V = (4/3) pi r^3

then

dV/dr = 4 pi r^2

and given that

dV/dt = 800 cm^3/min

and you require dr/dt (at r=30)

dV/dr = dV/dt . dt/dr

4 pi r^2 = 800 . dt/dr

4 pi (30)^2 /800 =dt/dr

800 / (4 pi 900) = dr/dt

0.0707 cm/min = dr/dt


hope this is correct.......
 
Related Rates

I'm having a problem getting the formula.

Gas is escaping from a spherical balloon at a rate of 10ft^3/hr. At what rate is the radius changing when the volume is 400ft^3?

I have V= 4/3 pi. r^3
and dv/dt= 10ft^3/hr

I know I need r= sqrt dv/4dt

I messing up somewhere.

Frances
 
Except for different numbers, your exercise is exactly the same as the original poster's. So follow the same logic and steps, inputting your numbers.

Eliz.

P.S. In future, please post new questions as new threads, not as replies to old threads, where they are frequently overlooked. Thank you.
 
I kept trying to take dy/dx of v=4/3 pi.r^3 (it was messy).

I got 400*3/4=pir^3

3rd sqrt (300/pi.)=r

-10/4pi. r^2=dr/dt

-5/2pi/r^2=dr/dt

-5/2pi. 3rd sqrt ((300/pi. )^2)=.038ft^3/hr
 
dy/dx?????
How about dv/dr which you got in part 1? Then
dr/dt = (dv/dt)/(dv/dr).

BTW: Look at your answer. dr/dt is feet per hour but you ended with ft^3/hr. You know you went astray. The units are not right.
 
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